The ACCUPLACER math placement test determines which math course you start in at college — and the gap between placing into developmental math and college-level math can cost a semester or more of time and tuition. This post gives you 30 practice questions with fully worked answers, organized by the three ACCUPLACER math test levels: Arithmetic, Quantitative Reasoning/Algebra/Statistics (QAS), and Advanced Algebra and Functions (AAF). Use these to find your current level and identify exactly which topics need the most work before your test date.
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Quick Guide to the Three ACCUPLACER Math Tests
| Test | Level | Who Takes It | Questions |
|---|---|---|---|
| Arithmetic | Foundational | Students placing into pre-algebra or developmental math | ~20 adaptive |
| QAS (Quantitative Reasoning, Algebra, and Statistics) | Intermediate | Students aiming for college-level non-STEM math | ~20 adaptive |
| AAF (Advanced Algebra and Functions) | Advanced | Students aiming for STEM or Calculus track | ~20 adaptive |
Part 1: Arithmetic Practice Questions (10 Questions)
The Arithmetic test covers whole numbers, fractions, decimals, percents, and order of operations at a foundational level.
1. Whole Numbers and Operations
Q: What is 348 ÷ 12?
A: 348 ÷ 12 = 29. Check: 12 × 29 = 12 × 30 − 12 = 360 − 12 = 348. ✓
2. Fractions
Q: Add: 3/8 + 5/6
A: LCD = 24. 9/24 + 20/24 = 29/24 = 1 5/24.
3. Fraction Division
Q: Divide: 3/4 ÷ 3/8
A: Multiply by the reciprocal: 3/4 × 8/3 = 24/12 = 2.
4. Decimals
Q: Multiply: 2.4 × 0.15
A: 24 × 15 = 360. Count decimal places: 1 + 2 = 3. Answer: 0.360 = 0.36.
5. Percents
Q: 18 is what percent of 72?
A: 18/72 × 100 = 25%. Answer: 25%.
6. Percent of a Number
Q: What is 35% of 200?
A: 0.35 × 200 = 70.
7. Order of Operations
Q: Evaluate: 4 + 3 × 2² − 5
A: Exponent first: 2² = 4. Multiply: 3 × 4 = 12. Then: 4 + 12 − 5 = 11.
8. Estimation
Q: Which is closest to 397 × 19: 700, 4,000, 7,000, or 8,000?
A: ≈ 400 × 20 = 8,000. Answer: 8,000.
9. Mixed Number Operations
Q: Subtract: 5 1/3 − 2 3/4
A: Convert to improper: 16/3 − 11/4. LCD = 12: 64/12 − 33/12 = 31/12 = 2 7/12.
10. Percent Change
Q: A price increases from $40 to $52. What is the percent increase?
A: Increase = $12. 12/40 × 100 = 30%.
Part 2: QAS Practice Questions (10 Questions)
The QAS covers ratios, proportions, basic algebra, coordinate geometry, data interpretation, and introductory statistics.
11. Ratios and Proportions
Q: A car travels 150 miles on 5 gallons of gas. How many miles can it travel on 8 gallons?
A: Unit rate = 30 mpg. 30 × 8 = 240 miles.
12. Linear Equations
Q: Solve: 5x − 7 = 3x + 9
A: 2x = 16 → x = 8.
13. Inequalities
Q: Solve: −3x + 4 ≤ 13. Represent the solution on a number line.
A: −3x ≤ 9 → x ≥ −3 (inequality flips when dividing by a negative). Solution: x ≥ −3. On the number line: closed circle at −3, shaded to the right.
14. Slope
Q: What is the slope of the line passing through (2, 5) and (6, 13)?
A: m = (13 − 5)/(6 − 2) = 8/4 = 2.
15. Linear Equations from a Graph
Q: A line crosses the y-axis at (0, 3) and has a slope of −2. What is the equation?
A: y = −2x + 3. Answer: y = −2x + 3.
16. Functions
Q: If f(x) = 3x² − x + 2, find f(−1).
A: f(−1) = 3(1) − (−1) + 2 = 3 + 1 + 2 = 6.
17. Data Interpretation
Q: A data set is 4, 7, 9, 11, 14, 15, 18. What is the median and the IQR?
A: Median = 11. Q1 = 7, Q3 = 15. IQR = 15 − 7 = 8.
18. Probability
Q: A bag has 4 red and 6 blue chips. You draw two chips without replacement. What is the probability both are red?
A: P = (4/10) × (3/9) = 12/90 = 2/15.
19. Systems of Equations
Q: Solve the system: y = 2x + 1 and y = −x + 7
A: 2x + 1 = −x + 7 → 3x = 6 → x = 2. y = 2(2) + 1 = 5. Answer: (2, 5).
20. Word Problem with Algebra
Q: Two planes leave the same airport at the same time traveling in opposite directions. One flies at 450 mph, the other at 380 mph. How many hours until they are 2,460 miles apart?
A: (450 + 380)t = 2,460 → 830t = 2,460 → t = about 2.96 hours ≈ 3 hours.
Part 3: Advanced Algebra and Functions (AAF) Practice Questions (10 Questions)
The AAF covers polynomial operations, factoring, quadratics, radical expressions, exponential and logarithmic functions, trigonometry basics, and complex rational expressions.
21. Polynomial Multiplication
Q: Expand: (2x − 3)(x + 5)
A: 2x² + 10x − 3x − 15 = 2x² + 7x − 15.
22. Factoring
Q: Factor: x² + 5x − 14
A: Find two numbers that multiply to −14 and add to 5: 7 and −2. Answer: (x + 7)(x − 2).
23. Quadratic Formula
Q: Solve using the quadratic formula: 2x² − 4x − 6 = 0
A: Divide by 2: x² − 2x − 3 = 0. Factor: (x − 3)(x + 1) = 0. Answer: x = 3 or x = −1.
24. Simplifying Radicals
Q: Simplify: √72
A: √72 = √(36 × 2) = 6√2. Answer: 6√2.
25. Rational Expressions
Q: Simplify: (x² − 9)/(x − 3)
A: x² − 9 = (x + 3)(x − 3). Cancel (x − 3): Answer: x + 3 (where x ≠ 3).
26. Exponential Functions
Q: A population of 1,000 grows at 5% per year. What is the population after 3 years? (Use the formula P = P₀(1 + r)ⁿ)
A: P = 1,000 × (1.05)³ = 1,000 × 1.157625 ≈ 1,158.
27. Logarithms
Q: Evaluate: log₂(32)
A: 2ˣ = 32 = 2⁵. Answer: 5.
28. Function Composition
Q: If f(x) = 2x + 1 and g(x) = x², find f(g(3)).
A: g(3) = 9. f(9) = 2(9) + 1 = 19.
29. Right Triangle Trigonometry
Q: In a right triangle, the angle θ has an opposite side of 5 and a hypotenuse of 13. What is sin(θ)?
A: sin(θ) = opposite/hypotenuse = 5/13.
30. Completing the Square
Q: Rewrite in vertex form: y = x² + 6x + 5
A: y = (x² + 6x + 9) + 5 − 9 = (x + 3)² − 4. Answer: y = (x + 3)² − 4. Vertex at (−3, −4).
Scoring Your Practice Set
| Section | Score | Interpretation |
|---|---|---|
| Arithmetic (Q1–10) | 8–10 correct | Ready to move past Arithmetic review |
| Arithmetic | Below 8 | Focus 70% of your prep time here first |
| QAS (Q11–20) | 8–10 correct | Solid intermediate-level readiness |
| QAS | Below 8 | Prioritize algebra and data review |
| AAF (Q21–30) | 8–10 correct | Solid college-level STEM math readiness |
| AAF | Below 8 | Focus on factoring, quadratics, and functions |
ACCUPLACER Math Resources
ViewMath publishes practice test books and study guides for the ACCUPLACER math assessments at all three levels. Each book includes topic-by-topic review sections, full practice tests, and complete worked solutions. Browse the full collection using the sidebar.
For a full format overview and study plan, see our post What Is on the ACCUPLACER Math Test?.
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